What remains to be done then, is to implement this idea. And here a variety of options are available. As mentioned above, one approach would be to follow Nelson, and earlier iterations of ED [1]}[2]}, by imposing that \(\phi (x)\) , or more conveniently \(\Phi (x)\) , be updated such that a global “energy" functional be conserved. The resulting dynamics was Hamiltonian, conferring the joint space, \(\left(\rho (x),\Phi (x)\right)\)  of dynamical variables with a canonical structure, i.e. a conserved symplectic form, Hamiltonian generators, Poisson brackets, etc. From here, one can go further towards obtaining a quantum dynamics by choosing an appropriate set of potentials in the Hamiltonian; namely, the quantum potential, familiar from Bohmian mechanics (see e.g. [3]}). But also, as previously mentioned, the reliance on a conserved energy is not conducive to further development of the theory, and thus this criterion fails.
